Problem: Simplify the following expression: $ a = \dfrac{3q + 2}{-10} + \dfrac{-7}{6} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{3q + 2}{-10} \times \dfrac{6}{6} = \dfrac{18q + 12}{-60} $ Multiply the second expression by $\dfrac{-10}{-10}$ $ \dfrac{-7}{6} \times \dfrac{-10}{-10} = \dfrac{70}{-60} $ Therefore $ a = \dfrac{18q + 12}{-60} + \dfrac{70}{-60} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{18q + 12 + 70}{-60} $ $a = \dfrac{18q + 82}{-60}$ Simplify the expression by dividing the numerator and denominator by -2: $a = \dfrac{-9q - 41}{30}$